{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Accumulated Local Effects for classifying flowers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example we will explain the behaviour of classification models on the Iris dataset. It is recommended to first read the [ALE regression example](ale_regression_california.ipynb) to familiarize yourself with how to interpret ALE plots in a simpler setting. Interpreting ALE plots for classification problems become more complex due to a few reasons:\n",
    "\n",
    " - Instead of one ALE line for each feature we now have one for each class to explain the feature effects towards predicting each class.\n",
    " - There are two ways to choose the prediction function to explain:\n",
    "   - Class probability predictions (e.g. `clf.predict_proba` in `sklearn`)\n",
    "   - Margin or logit predictions (e.g. `clf.decision_function` in `sklearn`)\n",
    "   \n",
    "We will see the implications of explaining each of these prediction functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.model_selection import train_test_split\n",
    "from alibi.explainers import ALE, plot_ale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load and prepare the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']\n",
      "['setosa' 'versicolor' 'virginica']\n"
     ]
    }
   ],
   "source": [
    "data = load_iris()\n",
    "feature_names = data.feature_names\n",
    "target_names = data.target_names\n",
    "X = data.data\n",
    "y = data.target\n",
    "print(feature_names)\n",
    "print(target_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Shuffle the data and define the train and test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fit and evaluate a logistic regression model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LogisticRegression(max_iter=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(max_iter=200)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(max_iter=200)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(max_iter=200)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y_test, lr.predict(X_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculate Accumulated Local Effects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are several options for explaining the classifier predictions using ALE. We define two prediction functions, one in the unnormalized logit space and the other in probability space, and look at how the resulting ALE plot interpretation changes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "logit_fun_lr = lr.decision_function\n",
    "proba_fun_lr = lr.predict_proba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "logit_ale_lr = ALE(logit_fun_lr, feature_names=feature_names, target_names=target_names)\n",
    "proba_ale_lr = ALE(proba_fun_lr, feature_names=feature_names, target_names=target_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "logit_exp_lr = logit_ale_lr.explain(X_train)\n",
    "proba_exp_lr = proba_ale_lr.explain(X_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ALE in logit space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We first look at the ALE plots for explaining the feature effects towards the unnormalized logit scores:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ale(logit_exp_lr, n_cols=2, fig_kw={'figwidth': 8, 'figheight': 5}, sharey=None);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the feature effects are linear for each class and each feature. This is exactly what we expect because the logistic regression is a linear model in the logit space.\n",
    "\n",
    "Furthermore, the units of the ALE plots here are in logits, which means that the feature effect at some feature value will be a positive or negative contribution to the logit of each class with respect to the mean feature effect."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the interpretation of the feature effects for \"petal length\" in more detail:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ale(logit_exp_lr, features=[2]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main insights from an ALE plot are qualitative—we can make several observations:\n",
    " - The slope of each ALE curve determines the relative effect of the feature `petal length` on the prediction (in logits) for each target class\n",
    " - In particular, we observe that the feature `petal length` has little relative variation in its effect towards the target class of `versicolor`\n",
    " - On the other hand, for the target classes of `setosa` and `virginica` the slopes of the curves are significant—the relative feature effect of `petal length` rises/falls for the target class of `virginica`/`setosa` as the `petal length` increases\n",
    " - The effect of `petal length` on the target classes of `setosa` and `virginica` are inversely related, suggesting that e.g. the effect of longer petal lengths contributes more positively towards predicting `virginica` and negatively towards predicting `setosa`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can gain even more insight into the ALE plot by looking at the class histograms for the feature `petal length`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "for target in range(3):\n",
    "    ax.hist(X_train[y_train==target][:,2], label=target_names[target]);\n",
    "\n",
    "ax.set_xlabel(feature_names[2])\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we see that the three classes are very well separated by this feature. This confirms that the ALE plot is behaving as expected—the feature effects of small value of `petal length` are that of increasing the logit values for the class `setosa` and decreasing for the other two classes. Also note that the range of the ALE values for this feature is particularly high compared to other features which can be interpreted as the model attributing more importance to this feature as it separates the classes well on its own."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ALE in probability space"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now turn to interpret the ALE plots for explaining the feature effects on the probabilities of each class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ale(proba_exp_lr, n_cols=2, fig_kw={'figwidth': 8, 'figheight': 5});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected, the ALE plots are no longer linear which reflects the non-linear nature due to the softmax transformation applied to the logits.\n",
    "\n",
    "Note that, in this case, the ALE are in the units of relative probability mass, i.e. given a feature value how much more (less) probability does the model assign to each class relative to the mean effect of that feature. This also means that any increase in relative probability of one class must result in a decrease in probability of another class. In fact, the ALE curves summed across classes result in 0 as a direct consequence of conservation of probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-5.551115123125783e-17\n",
      "1.734723475976807e-17\n",
      "-6.661338147750939e-16\n",
      "4.440892098500626e-16\n"
     ]
    }
   ],
   "source": [
    "for feature in range(4):\n",
    "    print(proba_exp_lr.ale_values[feature].sum())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By transforming the ALE plots into probability space we can gain additional insight into the model behaviour. For example, the ALE curve for the feature `petal width` and class `setosa` is virtually flat. This means that the model does not use this feature to assign higher or lower probability to class `setosa` with respect to the average effect of that feature. This is not readily seen in logit space as the ALE curve has negative slope which would lead us to the opposite conclusion. The interpretation here is that even though the ALE curve in the logit space shows a negative effect with feature value, the effect in the logit space is not significant enough to translate into a tangible effect in the probability space.\n",
    "\n",
    "Turning to the feature `petal length` we can observe a much more nuanced behaviour of the ALE plots than we saw in the logit space previously. In particular, for the target class `versicolor`, whilst the ALE curve is nearly flat in the logit space, in probability space it reveals a significant uplift over the average effect of `petal length` towards predicting `versicolor` in an interval between `~3-5cm`. This agrees with our observation previously that the histogram of `petal length` by target class reveals that the feature can separate all three classes quite well.\n",
    "\n",
    "Finally, the feature `sepal width` does not offer significant information to the model to prefer any class over the other (with respect to the mean effect of `sepal_width` that is). If we plot the marginal distribution of `sepal_width` it explains why that is—the overlap in the class conditional histograms of this feature show that it does not increase the model discriminative power:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "for target in range(3):\n",
    "    ax.hist(X_train[y_train==target][:,1], label=target_names[target]);\n",
    "\n",
    "ax.set_xlabel(feature_names[1])\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ALE for gradient boosting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we look at the resulting ALE plots for a highly non-linear model—a gradient boosted classifier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.ensemble import GradientBoostingClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>GradientBoostingClassifier()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">GradientBoostingClassifier</label><div class=\"sk-toggleable__content\"><pre>GradientBoostingClassifier()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "GradientBoostingClassifier()"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gb = GradientBoostingClassifier()\n",
    "gb.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy_score(y_test, gb.predict(X_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As before, we explain the feature contributions in both logit and probability space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "logit_fun_gb = gb.decision_function\n",
    "proba_fun_gb = gb.predict_proba"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "logit_ale_gb = ALE(logit_fun_gb, feature_names=feature_names, target_names=target_names)\n",
    "proba_ale_gb = ALE(proba_fun_gb, feature_names=feature_names, target_names=target_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "logit_exp_gb = logit_ale_gb.explain(X_train)\n",
    "proba_exp_gb = proba_ale_gb.explain(X_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ALE in logit space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ale(logit_exp_gb, n_cols=2, fig_kw={'figwidth': 8, 'figheight': 5});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The ALE curves are no longer linear as the model used is non-linear. Furthermore, we've plotted the ALE curves of different features on the same scale on the $y$-axis which suggests that the features `petal length` and `petal width` are more discriminative for the task. Checking the feature importances of the classifier confirms this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00221272, 0.01651258, 0.51811252, 0.46316218])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gb.feature_importances_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ALE in probability space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ale(proba_exp_gb, n_cols=2, fig_kw={'figwidth': 8, 'figheight': 5});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because of the non-linearity of the gradient boosted model the ALE curves in probability space are very similar to the curves in the logit space just on a different scale."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparing ALE between models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have seen that for both logistic regression and gradient boosting models the features `petal length` and `petal width` have a high feature effect on the classifier predictions. We can explore this in more detail by comparing the ALE curves for both models. In the following we plot the ALE curves of the two features for predicting the class `setosa` in probability space:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(8, 4), sharey='row');\n",
    "plot_ale(proba_exp_lr, features=[2, 3], targets=['setosa'], ax=ax, line_kw={'label': 'LR'});\n",
    "plot_ale(proba_exp_gb, features=[2, 3], targets=['setosa'], ax=ax, line_kw={'label': 'GB'});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this plot we can draw a couple of conclusions:\n",
    "\n",
    " - Both models have similar feature effects of `petal length`—a high positive effect for predicting `setosa` for small feature values and a high negative effect for large values (over >3cm).\n",
    " - While the logistic regression model does not benefit much from the `petal width` feature to discriminate the `setosa` class, the gradient boosted model does exploit this feature to discern between different classes."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
